It is a while since we discussed the matter, so let us remind ourselves of what this means. We have a population whose males are undergoing evolution of some characteristic such as tail length in widow birds, under the influence of female preference tending to make the tails longer and utilitarian selection tending to make the tails shorter. The reason there is any momentum in the evolution towards longer tails is that, whenever a female chooses a male of the type she 'likes', she is, because of the nonrandom association of genes, choosing copies of the very genes that made her do the choosing. So, in the next generation, not only will the males tend to have longer tails, but the females will tend to have a stronger preference for long tails. It is not obvious which of these two incremental processes will have the highest rate, generation by generation. We have so far considered the case where tail length increases faster, per generation, than preference. Now we come to consider the other possible case, where preference increases at an even higher rate, per generation, than tail length itself does. In other words, we are now going to discuss the case where the choice discrepancy gets bigger as the generations go by, not smaller as in the previous paragraphs.
Here the theoretical consequences are even more bizarre than before. Instead of negative feedback, we have positive feedback. As the generations go by, tails get longer, but the female desire for long tails increases at a higher rate. This means that, theoretically, tails will get even longer still, and at an ever-accelerating rate as the generations go by. Theoretically, tails will go on expanding even after they are 10 miles long. In practice, of course, the rules of the game will have been changed long before these absurd lengths are reached, just as our steam engine with its reversed Watt governor would not really have gone on accelerating to a million revolutions per second. But although we have to water down the conclusions of the mathematical model when we come to the extremes, the model's conclusions may well hold true over a range of practically plausible conditions.
Now, 50 years late, we can understand what Fisher meant, when he baldly asserted that 'it is easy to see that the speed of development will be proportional to the development already attained, which will therefore increase with time exponentially, or in geometric progression'. His rationale was clearly the same as Lande's, when he said: 'The two characteristics affected by such a process, namely plumage development in the male, and sexual preference for such developments in the female, must thus advance together, and so long as the process is unchecked by severe counterselection, will advance with ever-increasing speed'
